We consider a piecewise linear, discontinuous Galerkin method for the time discretization of a fractional diffusion equation involving a parameter in the range −1 < α < 0. Our analysis shows that, for a time interval (0, T) and a spatial domain Ω, the uniform error in L∞((0, T); L2(Ω)) is of order kρ, where ρ = ming(2, +α) and k denotes the maximum time step. Thus, if −½ ≤ α < 0, then we have optimal 𝒪(k2) convergence, just as for the classical diffusion (heat) equation.